On the Mellin transforms of powers of Hardy's function.Article

• 1 Katedra Matematike

Various properties of the Mellin transform function

$$\mathcal{M}_k(s):= \int_1^{\infty} Z^k(x)x^{-s}\,dx$$ are investigated, where $$Z(t):=\zeta(\frac{1}{2}+it)\,\chi(\frac{1}{2}+it)^{-1/2},~~~~\zeta(s)=\chi(s)\zeta(1-s)$$ is Hardy's function. Connections with power moments of $|\zeta(\frac{1}{2}+it)|$ are established, and natural boundaries of $\mathcal{M}_k(s)$ are discussed.

---

Download this fileSee the document's page on HAL